# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
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### Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
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### Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
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### How to do numerical line integral? [closed]

I have a 2D numeric (interpolating) function J that represents the current density of a square plate. I'd like to integrate J along one edge to find the total current coming out of that side. I'm ...
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### AbsoluteTiming of nested integration gives strange result

I found somewhat strange behaviour of nested integration timings. Consider the following code: ...
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### Getting an error with NIntegrate due to insufficient WorkingPrecision or divergent integral

Hello I have the following problem. But when I try to solve it, I get an error saying 'Catastrophic loss of precision in the global error estimate due to \ insufficient WorkingPrecision or divergent ...
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### NDSolve problem in Mathematica 10.1, possible bug

The following code, ...
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### NDSolve for a system of nonlinear coupled pde

I try to solve a system($n$) of coupled nonlinear 1-d PDE's which is basically coupled sine-Gordon equations (through 2nd spatial derivative) in time and space. I am interested in the dynamics when I ...
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### Optimizing NMinimization and NIntegration with a Nested List-Valued Function

I want to use NMinimize and NIntegrate on each element of a nested list-valued function. Here's a simple example of what I'm ...
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### Numerical integration plot

I am trying to do a numerical integration plot in Mathematica. Specifically, I want to plot $r$ versus $\tau$ where, $$\frac{dr}{d\tau}=\sqrt{2F(r)}$$ $F$ being a quartic polynomial. The limit of $r$ ...
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### difficulty in numerical estimate of double integral

I entered the following simple integral in mathematica: ...
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### Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the ...
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### Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
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### Replace variable with value prior to evaluating NIntegrate

The title says it all. Reading posts such as this however, I'm not seeing how to do this. This is the simplest example that can show my problem. ...
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### Nested Numerical Integration [duplicate]

So I am trying to evalute the following Integral Numerically: $$\int_{\mathcal{J}^+(x_0)\cap\mathcal{J}^-(x_f)}^{}A(x_0,x_1)\int_{\mathcal{J}^+(x_1)\cap\mathcal{J}^-(x_f)}^{}A(x_1,x_2) dx_1dx_2$$ ...
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### How to find the integrand singularity points when having NIntegrate::slwcon:

In order to calculate the closed area of the curve below defined by parametric equation curve02, ...
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### My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
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### ND on a function using NIntegrate

I need to numerically differentiate a function that takes a list as an argument and that uses NIntegrate in its definition. A simple example is ...
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### Numerical Integral with Boolean as part of argument

I am trying to numerically calculate a partial surface area integral of an oblate spheroid in spherical coordinates. The area I want to calculate is determined by a boolean function in the argument of ...
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### Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
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### How can I automatically set an NIntegrate call to zero if NIntegrate::slwcon is observed?

This is a generic question about the NIntegrate function. I am attempting to numerically integrate a function which may or may not be highly oscillatory, based on it's inputs. For a certain sets of ...
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### Discontinuous boundary condition in NDSolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $\cases{ U[0,y,t]=0,& if$0&...
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### Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
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### Maximum of an integral that depends on a parameter [duplicate]

I have defined a function f(x,t) : ...
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### Force WhenEvent to respect default stepsize

I have to numerically integrate an equation system and monitor the accumulating datapoints. For example, I fit a line to a subsample of the points and terminate via ...
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### What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?

I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that ...
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### Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
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### Difficulty using NDSolve

I am tying to solve two differential equations with two delays numerically. The result didn't come out and it was written that “NDSolve::ndsz:...step size is effectively zero; singularity or stiff ...
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### NFourierTransform do not show all points, even change PlotPoints and Exclusions

Needs["FourierSeries`"] I try solve the numerical Fourier transform of this function: ...
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### NIntegrate a function in a circular segment

I am trying to integrate numerically a function over a circular segment surface using polar coordinates. In the following example I am using the zero order Bessel function, but any cylindrical ...
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### Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
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### WorkingPrecision and AccuracyGoal for using with NIntegrate

I'm modeling a quantum tunneling barrier. Because I want to express my quantities in mks units, that means that some of the variables I'm using are pretty small (10^-9). I use NIntegrate for part of ...
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### Numerical approximation using trapezoidal formula [closed]

I have bumped into a problem, that I cannot solve. I have to approximate the value of ln3 using a composite trapezoidal formula, so that the error should be within (10)^-3! How can it be solved?
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### Trying to find a temperature profile with a nonlinear 2nd order ODE. NDSolve very sensitive to seemingly arbitrary constant

I am trying to solve this differential equation for a heat transfer problem: kt\frac{\partial^2 T}{\partial x^2} = \epsilon \sigma T^4, \ \ \ T(0) = T_0, \ \ \ \frac{\partial T}{\...